NOTE ADDED JULY 2005: This page describes a method by which the location of the MER rovers could have been determined, using data from the Mars Relay on Mars Global Surveyor. However, the approach was not needed because the rover team quickly determined where the rovers were located, and this was followed within days by acquisition of Mars Global Surveyor Mars Orbiter Camera images that actually showed the hardware on the surface. The reader of this section should understand that this information has been superseded by actual events.

One of the more important science activities that will
be conducted during the first few days that the Mars Exploration Rovers
(MERs) are on the surface of Mars will be to determine the exact location
of the landing site. Locating the landers is important for a couple of reasons.
First, it allows the science team to begin planning where the rover will
travel during its 90+ sol mission. Second, it allows scientists to place
their findings within a regional and global context provided by orbiter
observations.

As part of the Mars Global Surveyor (MGS)
Mars Orbiter Camera (MOC) investigation, Malin Space Science
Systems (MSSS) will attempt
to locate the rovers using data from the MGS Mars Relay (MR) antenna and
MOC instrument. These efforts fall
into three areas: (1) radiolocation of the landers using doppler measurements
performed by the Mars Relay, (2) sightline identification of features seen
in MOC high-resolution, narrow angle camera images once a rough location
within the landing area has been identified via step 1, and (3) identification
of the rover in new, 50-cm/pixel orbiter images acquired during the rover
mission.

Radiolocation of the MER Landers using MR Doppler

The Mars Relay (MR) system
acquires three doppler measurement every BTTS
(16 seconds). During the MGS's pass over the landing site during MER
Entry, Descent, and Landing (EDL), when the MER is communicating to the
MR, only about 4 or 5 BTTS's will be recorded, or perhaps 12-15 doppler
measurements. To analyse the doppler measurements, Scott Davis of MSSS devised
a simple process: for each time along the MGS orbit where a doppler measurement
is made, he calculates what the doppler signal would be from each longitude,
latitude, and altitude within the landing ellipse if that location were
in fact the actual location of the lander. He then compares these synthetic
values with the actual value measured at that time by the MR. Figure 1 shows
a typical MGS early-morning orbit pass by the MER-A landing site in Gusev Crater

Figure 1: Typical "AM" pass of MGS relative to MER-A landing
site. MGS would follow the white line from north (top) to south at around
2 AM local solar time.

Figure 2 shows single-location maps of the differences
between the synthetic and "actual" values (generated in a test
of the system) for three times when MGS was approaching (A), passing (B),
and receding (C) from the landing location. The three examples were taken
near the limits of communication (just after contact is established and
just before it is lost). Faint gray lines that alternate light and dark
indicate contours of values offset from their neighbors by 256. The white
lines are the locus of points along which the minium differences occur--the
lander lies somewhere along each white line.

Figure 2: Color-coded differrence between actual doppler value and
synthetic doppler values computed for each location in the map. Red denotes
small differences, blue large differences. The lander would be at the lowest
value, which for a single measurement is a line of points

As with the common phenomenon of parallax (look at a
object close to you with one eye closed, then open that eye and close the
other... the object shifts position in your field of view because of the
separation between your two eyes), multiple doppler measurements provide
additional
information than any single measurement alone. Figure 3 shows how the three
separate measurments shown in Figure 2 can be used to locate the lander...
it is at the intersection of the three loci of possible locations. The
uncertaintly at this point is probably not as good as the lines imply;
in reality, the lines are a kilometer or more wide (this is a function
of the location prediction
for the MGS orbiter and the precision with which the doppler frequency is
being measured). On the basis of these data, however, we could with high
confidence say (in this test case) that the landing occurred in the eastern
half of the ellipse, and probably south of the center-line.

Figure 3: Intersection of the loci of possible locations (based on
the minimum difference between synthetic doppler and "actual"
doppler measurement) for three separate doppler measurement locations in
the MGS orbit.

The MGS MOC has
two early opportunities to use radiolocation
to find each MER lander. The first comes on the day of landing, during the
entry, descent, and landing (EDL) pass. Because the rover is expected to
communicate with MGS only for about 80-85 seconds (at most) before touching
down, doppler measurements will be limited by two factors: first, the MR
only takes 3 measurements per 16-second BTTS, so only 12-15 measurements
will be made during EDL. Second, since the orbiter only moves about 300
km in this time, the "parallax angle" between these measurements
will be small, so there will be more ambiguity in the location. Figurer
4 shows what a 15 measurement location map might look like.

Figure 4: Possible EDL doppler results from 15 measurements over an
80-85 second period around landing. Location uncerrtainty is several kilometers.

A much better opportunity occurs about 12 hours later,
during the first MGS "AM" pass. At this time, the lander will
communicate with the orbiter for 6 to 10 minutes (later passes may last
as long as 20 minutes). In a 6-minute pass, almost 70 doppler measurements
will be made, greatly increasing the "parallax" angle and reducing
by statistical averaging errors resulting from frequency sampling. An example
of a Sol 2, 2 AM pass doppler map is shown in Figure 5. Location precision
is probably better than 1 km and depends mostly on MGS spacecraft location
prediction (which have been good to several 100 meters). About a day or
two after landing, the MGS tracking data will be available and a refined
location will be calculated.

Sightline Analyses: Matching Horizon Features with Features
seen from Orbit

From the radiolocation analysis described above, we
will have a good place to start looking for features to match between early
panorama images taken within the first few sols of surface activity and
orbiter images taken before landing. This process is pretty straight forward
in areas where good relief is visible, but in areas of very low relief or
homogenous morphology (every place looks the same), sight-line analysis
can be complicated or even defeated. Below we show an example of sightline
analysis for the 1997 lander, Mars Pathfinder.

One begins with a parorama view of the landing site.
Figure 6 is a pan taken by the Imager for Mars Pathfinder (IMP) early in
the Pathfinder mission. Figure 7 shows a stereographic reprojection of that
mosaic, which simulates an overhead perspective. In this view, it is easy
to see and draw sight-lines between the center of the lander and horizon
and sub-horizon features.

By placing the stereographic projection of the lander
mosaic with sight-lines on top of a similarly-projected MOC image, one can
move the lander mosaic around until sightlines match the overhead morphology.
Figure 8 shows this match for the Pathfinder site.

Figure 8: Pathfinder mosaic in stereographic projection superimposed
on MOC high resolution image, also in stereographic projection. The former
was moved relative to the latter until the sightlines projected to the correct
large-scale features.

Working with the MGS Spacecraft Team at Lockheed Martin,
and MGS Project management and mission planning at the Jet Propulsion
Laboratory (JPL), a new imaging technique
for improving MOC high resolution images has been devised using the technique
of image motion compensation, or IMC. IMC changes the spacecraft pointing
at an angular rate comparable to the spacecraft orbital motion to allow
the MOC line to dwell longer on a given portion of the planet. This improves
the signal to noise ratio (SNR) and, by changing the sampling rate, the
spatial resolution in the downtrack direction (the crosstrack direction
is fixed by the nature of the detector in the narrow angle camera). Here's
how it works:

At a nominal altitude of 400 km, and for a nominal orbital
period of 117 minutes, the orbital speed of the spacecraft is about 3.4
km/sec. If the spacecraft didn't rotate in pitch, the nadir would only point
towards the planet at one point in the orbit, so the spacecraft rotates
at a rate of 360° in 117 minutes, or 0.9 mrad/sec. Projocted at the
surface from 400 km altitude, this is equivalent to a reduction in the orbital
rate of just over 0.3 km/sec, yielding a ground speed of 3.04 km/sec.

Under normal operations, MOC images must account for
these combined motions. As a line-scan system, each line of a MOC image
must be exposed and read out before the next line can be taken. If the line
time is longer than the equivalent resolution (the "instantaneous"
field of view-IFOV--or projected pixel size), then the image resolution
is degraded. If the line time is shorter than the equivalent resolution,
then the image resolution can be increased in the down-track direction.
The cross-track dimension is always equivalent to the IFOV. At a ground
speed of 3.04 km/sec and for a projected pixel size of just under 1.5 m/pixel
(3.7E-01 IFOV * 400 km), the line time is 1.5 m/3050 m/sec ~ 0.48 msec.
This is essentially the fastest line time that the MOC can take images,
because it was designed to get square pixels and take as much time as it
could per line in order to get the best SNR it could.

By pitching the spacecraft faster than it needs to just
maintain nadir orientation, the "effective" ground speed can be
reduced by a proportionally larger amount than the 0.3 km/sec required for
nadir pointing. Figure 9 shows the relationship between rotation
rate in mrad/sec and the equivalent spatial sampling at the MOC's nominal
line rater of 0.48 msec/line. At 5 mrad/sec, the sampling scale is about
70 cm/pixel, at 6 mrad/sec it is 50 cm/pixel, and at 7 mrad/sec, the sampling
is 30 cm/pixel. MOC resolution is limited by diffraction at about 70 cm/pixel.
However, the 2005 Mars Reconnaissance Orbiter (MRO) High Resolution Imaging
Science Experiment (HiRISE) experiment is predicated on using internal image
motion compensation to provide sampling at smaller scales than its diffraction
limit and using image processing techniques to improve the resolution; these
same techniques can be employed on MOC images taken at sampling scales smaller
than 70 cm. In addition, rather than keeping the sampling rate at
0.48 msec/line, we can increase the line time to collect more photons, thus
increasing our signal-to-noise (SNR).
A practical compromise between sampling and SNR is to
maintain a ground sampling distance of 50 cm (oversampling the MOC diffraction
point spread function) and increasing the line time by a factor of 3 (this
improves SNR by 3½, or 1.73).

Figure 9: Relationship between Ground Sampling and IMC
S/C Motion

The "down" side to IMC images is that more
lines must be taken to cover a specific distance on the ground (in practice,
we're taking 3 times the number of pixels). The MOC is limited in the size
of images it can take to the size of its buffer, about 80 Mbits. Realtime
(40 Mbps) lossless compression helps, but IMC images generally cover much
less ground than normal MOC high resolution images.

Another issue that must be addressed is that of planetary
rotation. Figure 10 shows the impact of planetary rotation on the shape
of the area covered by an image as the effective spacecraft ground speed
is reduced by pitch IMC. The high distortion works to reduce the improvements
gained by higher sampling. To counteract this effect, the Spacecraft Team
devised an approach to include planetary rotation compensation as well as
spacecraft velocity compensation.

Figure 10: Image footprint distortion caused by planetary rotation
for different amounts of spacecraft velocity compensation. 7.66 mr/sec is
the compromise value most recently used in IMC test imaging.

IMC Lander Imaging Test: Pathfinder

So, does this work? To find out, we have taken a small
number of test images, including of the Viking 1 and Pathfinder landing
sites. Figure 11 shows a comparison of enlargements of the best view of
the Pathfinder site taken without IMC and with the new, IMC image. You'll
have to look at the large version, the differences are really at the pixel-level.
Three effects are noticable in the right-hand (new, IMC) image:

The SNR is better (you see less "salt-and-pepper"
1-pixel spots in the image relative to the left-hand image).

The noise pixels that do occur are physically smaller,
making them less noticable.

The image is higher resolution, as can be seen in
looking at the rocks around the crater in the lower left of each image.

Figure 11: Comparison of "normal" MOC high resolution image,
taken at roughly 1.4 m/pixel and shown here at 0.6 m/pixel, and "IMC"
image taken at a ground sampling distance of 0.5 m/pixel and shown here
at 0.6 m/pixel.

Of course, the proof lies in whether or not we can actually
see the Pathfinder lander. Figure 12 shows the lander panorama stereographic
projection with sightlines to distant horizon features, and the location
at which the sightlines converge. Multi-pixel features at the convergence
of the sightlines are interpreted to be the Pathfinder spacecraft and the
rock "Yogi" several meters north of the lander.